1 Answer
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Problematic uses of terminology

Where Oracle describes first Java for "your operating system" then "for your computer", the download is more accurately only for things that use the Internet plug-in:

jre-7u13-macosx-x64.dmg installs what's required for that plug-in, but for things that use Java without the plug-in, this installer from Oracle does nothing.

Hint

On OS X: if you want a Java Runtime Environment (JRE) from Oracle to be like the JRE in the diagram below for both (a) things that use the Internet plug-in and (b) things that use Java without that plug-in: